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Determine which of the following functions are linear transformations? 1. T: P, → P2; T(p(x)) = x² ++ p(x) 2. S : R → R; S(r) = x 3. R: R → R²; R(r, y) = (r,-y) 4. M : Mnn → R; M(A) = A" (transposition) 5. N: Mnn → R; N(A) = rank A Select one or more: O a. N Ob. S OcR C. R O d. M Oe. T

Determine which of the following functions are linear transformations? 1. T: P, → P2; T(p(x)) = x² ++ p(x) 2. S : R → R; S(r) = x 3. R: R → R²; R(r, y) = (r,-y) 4. M : Mnn → R; M(A) = A" (transposition) 5. N: Mnn → R; N(A) = rank A Select one or more: O a. N Ob. S OcR C. R O d. M Oe. T

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine which of the following functions are linear transformations? 1.T: P, → P2; T(p(x)) = z² + p(z) 2. S: R → R; S(r) = x 3. R: R? → R²; R(r, y) = (x,-y) 4. M : Man → R; M(A) = A" (transposition) 5. N: Mnn → R; N(A) = rank A Select one or more: 口 a. N Ob. S OC. R O d. M e. T
Transcribed Image Text:Determine which of the following functions are linear transformations? 1.T: P, → P2; T(p(x)) = z² + p(z) 2. S: R → R; S(r) = x 3. R: R? → R²; R(r, y) = (x,-y) 4. M : Man → R; M(A) = A" (transposition) 5. N: Mnn → R; N(A) = rank A Select one or more: 口 a. N Ob. S OC. R O d. M e. T
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